// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

// Function void Eigen::AlignedBox::transform(const Transform& transform)
// is provided under the following license agreement:
//
// Software License Agreement (BSD License)
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#ifndef EIGEN_ALIGNEDBOX_H
#define EIGEN_ALIGNEDBOX_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
 *
 *
 * \class AlignedBox
 *
 * \brief An axis aligned box
 *
 * \tparam _Scalar the type of the scalar coefficients
 * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
 *
 * This class represents an axis aligned box as a pair of the minimal and maximal corners.
 * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using
 * isEmpty(). \sa alignedboxtypedefs
 */
template<typename _Scalar, int _AmbientDim>
class AlignedBox
{
  public:
	EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar, _AmbientDim)
	enum
	{
		AmbientDimAtCompileTime = _AmbientDim
	};
	typedef _Scalar Scalar;
	typedef NumTraits<Scalar> ScalarTraits;
	typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
	typedef typename ScalarTraits::Real RealScalar;
	typedef typename ScalarTraits::NonInteger NonInteger;
	typedef Matrix<Scalar, AmbientDimAtCompileTime, 1> VectorType;
	typedef CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> VectorTypeSum;

	/** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
	enum CornerType
	{
		/** 1D names @{ */
		Min = 0,
		Max = 1,
		/** @} */

		/** Identifier for 2D corner @{ */
		BottomLeft = 0,
		BottomRight = 1,
		TopLeft = 2,
		TopRight = 3,
		/** @} */

		/** Identifier for 3D corner  @{ */
		BottomLeftFloor = 0,
		BottomRightFloor = 1,
		TopLeftFloor = 2,
		TopRightFloor = 3,
		BottomLeftCeil = 4,
		BottomRightCeil = 5,
		TopLeftCeil = 6,
		TopRightCeil = 7
		/** @} */
	};

	/** Default constructor initializing a null box. */
	EIGEN_DEVICE_FUNC inline AlignedBox()
	{
		if (EIGEN_CONST_CONDITIONAL(AmbientDimAtCompileTime != Dynamic))
			setEmpty();
	}

	/** Constructs a null box with \a _dim the dimension of the ambient space. */
	EIGEN_DEVICE_FUNC inline explicit AlignedBox(Index _dim)
		: m_min(_dim)
		, m_max(_dim)
	{
		setEmpty();
	}

	/** Constructs a box with extremities \a _min and \a _max.
	 * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is
	 * empty. */
	template<typename OtherVectorType1, typename OtherVectorType2>
	EIGEN_DEVICE_FUNC inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max)
		: m_min(_min)
		, m_max(_max)
	{
	}

	/** Constructs a box containing a single point \a p. */
	template<typename Derived>
	EIGEN_DEVICE_FUNC inline explicit AlignedBox(const MatrixBase<Derived>& p)
		: m_min(p)
		, m_max(m_min)
	{
	}

	EIGEN_DEVICE_FUNC ~AlignedBox() {}

	/** \returns the dimension in which the box holds */
	EIGEN_DEVICE_FUNC inline Index dim() const
	{
		return AmbientDimAtCompileTime == Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime);
	}

	/** \deprecated use isEmpty() */
	EIGEN_DEVICE_FUNC inline bool isNull() const { return isEmpty(); }

	/** \deprecated use setEmpty() */
	EIGEN_DEVICE_FUNC inline void setNull() { setEmpty(); }

	/** \returns true if the box is empty.
	 * \sa setEmpty */
	EIGEN_DEVICE_FUNC inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }

	/** Makes \c *this an empty box.
	 * \sa isEmpty */
	EIGEN_DEVICE_FUNC inline void setEmpty()
	{
		m_min.setConstant(ScalarTraits::highest());
		m_max.setConstant(ScalarTraits::lowest());
	}

	/** \returns the minimal corner */
	EIGEN_DEVICE_FUNC inline const VectorType&(min)() const { return m_min; }
	/** \returns a non const reference to the minimal corner */
	EIGEN_DEVICE_FUNC inline VectorType&(min)() { return m_min; }
	/** \returns the maximal corner */
	EIGEN_DEVICE_FUNC inline const VectorType&(max)() const { return m_max; }
	/** \returns a non const reference to the maximal corner */
	EIGEN_DEVICE_FUNC inline VectorType&(max)() { return m_max; }

	/** \returns the center of the box */
	EIGEN_DEVICE_FUNC inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(VectorTypeSum, RealScalar, quotient)
		center() const
	{
		return (m_min + m_max) / RealScalar(2);
	}

	/** \returns the lengths of the sides of the bounding box.
	 * Note that this function does not get the same
	 * result for integral or floating scalar types: see
	 */
	EIGEN_DEVICE_FUNC inline const CwiseBinaryOp<internal::scalar_difference_op<Scalar, Scalar>,
												 const VectorType,
												 const VectorType>
	sizes() const
	{
		return m_max - m_min;
	}

	/** \returns the volume of the bounding box */
	EIGEN_DEVICE_FUNC inline Scalar volume() const { return sizes().prod(); }

	/** \returns an expression for the bounding box diagonal vector
	 * if the length of the diagonal is needed: diagonal().norm()
	 * will provide it.
	 */
	EIGEN_DEVICE_FUNC inline CwiseBinaryOp<internal::scalar_difference_op<Scalar, Scalar>,
										   const VectorType,
										   const VectorType>
	diagonal() const
	{
		return sizes();
	}

	/** \returns the vertex of the bounding box at the corner defined by
	 * the corner-id corner. It works only for a 1D, 2D or 3D bounding box.
	 * For 1D bounding boxes corners are named by 2 enum constants:
	 * BottomLeft and BottomRight.
	 * For 2D bounding boxes, corners are named by 4 enum constants:
	 * BottomLeft, BottomRight, TopLeft, TopRight.
	 * For 3D bounding boxes, the following names are added:
	 * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil.
	 */
	EIGEN_DEVICE_FUNC inline VectorType corner(CornerType corner) const
	{
		EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE);

		VectorType res;

		Index mult = 1;
		for (Index d = 0; d < dim(); ++d) {
			if (mult & corner)
				res[d] = m_max[d];
			else
				res[d] = m_min[d];
			mult *= 2;
		}
		return res;
	}

	/** \returns a random point inside the bounding box sampled with
	 * a uniform distribution */
	EIGEN_DEVICE_FUNC inline VectorType sample() const
	{
		VectorType r(dim());
		for (Index d = 0; d < dim(); ++d) {
			if (!ScalarTraits::IsInteger) {
				r[d] = m_min[d] + (m_max[d] - m_min[d]) * internal::random<Scalar>(Scalar(0), Scalar(1));
			} else
				r[d] = internal::random(m_min[d], m_max[d]);
		}
		return r;
	}

	/** \returns true if the point \a p is inside the box \c *this. */
	template<typename Derived>
	EIGEN_DEVICE_FUNC inline bool contains(const MatrixBase<Derived>& p) const
	{
		typename internal::nested_eval<Derived, 2>::type p_n(p.derived());
		return (m_min.array() <= p_n.array()).all() && (p_n.array() <= m_max.array()).all();
	}

	/** \returns true if the box \a b is entirely inside the box \c *this. */
	EIGEN_DEVICE_FUNC inline bool contains(const AlignedBox& b) const
	{
		return (m_min.array() <= (b.min)().array()).all() && ((b.max)().array() <= m_max.array()).all();
	}

	/** \returns true if the box \a b is intersecting the box \c *this.
	 * \sa intersection, clamp */
	EIGEN_DEVICE_FUNC inline bool intersects(const AlignedBox& b) const
	{
		return (m_min.array() <= (b.max)().array()).all() && ((b.min)().array() <= m_max.array()).all();
	}

	/** Extends \c *this such that it contains the point \a p and returns a reference to \c *this.
	 * \sa extend(const AlignedBox&) */
	template<typename Derived>
	EIGEN_DEVICE_FUNC inline AlignedBox& extend(const MatrixBase<Derived>& p)
	{
		typename internal::nested_eval<Derived, 2>::type p_n(p.derived());
		m_min = m_min.cwiseMin(p_n);
		m_max = m_max.cwiseMax(p_n);
		return *this;
	}

	/** Extends \c *this such that it contains the box \a b and returns a reference to \c *this.
	 * \sa merged, extend(const MatrixBase&) */
	EIGEN_DEVICE_FUNC inline AlignedBox& extend(const AlignedBox& b)
	{
		m_min = m_min.cwiseMin(b.m_min);
		m_max = m_max.cwiseMax(b.m_max);
		return *this;
	}

	/** Clamps \c *this by the box \a b and returns a reference to \c *this.
	 * \note If the boxes don't intersect, the resulting box is empty.
	 * \sa intersection(), intersects() */
	EIGEN_DEVICE_FUNC inline AlignedBox& clamp(const AlignedBox& b)
	{
		m_min = m_min.cwiseMax(b.m_min);
		m_max = m_max.cwiseMin(b.m_max);
		return *this;
	}

	/** Returns an AlignedBox that is the intersection of \a b and \c *this
	 * \note If the boxes don't intersect, the resulting box is empty.
	 * \sa intersects(), clamp, contains()  */
	EIGEN_DEVICE_FUNC inline AlignedBox intersection(const AlignedBox& b) const
	{
		return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max));
	}

	/** Returns an AlignedBox that is the union of \a b and \c *this.
	 * \note Merging with an empty box may result in a box bigger than \c *this.
	 * \sa extend(const AlignedBox&) */
	EIGEN_DEVICE_FUNC inline AlignedBox merged(const AlignedBox& b) const
	{
		return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max));
	}

	/** Translate \c *this by the vector \a t and returns a reference to \c *this. */
	template<typename Derived>
	EIGEN_DEVICE_FUNC inline AlignedBox& translate(const MatrixBase<Derived>& a_t)
	{
		const typename internal::nested_eval<Derived, 2>::type t(a_t.derived());
		m_min += t;
		m_max += t;
		return *this;
	}

	/** \returns a copy of \c *this translated by the vector \a t. */
	template<typename Derived>
	EIGEN_DEVICE_FUNC inline AlignedBox translated(const MatrixBase<Derived>& a_t) const
	{
		AlignedBox result(m_min, m_max);
		result.translate(a_t);
		return result;
	}

	/** \returns the squared distance between the point \a p and the box \c *this,
	 * and zero if \a p is inside the box.
	 * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&)
	 */
	template<typename Derived>
	EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const;

	/** \returns the squared distance between the boxes \a b and \c *this,
	 * and zero if the boxes intersect.
	 * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&)
	 */
	EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const AlignedBox& b) const;

	/** \returns the distance between the point \a p and the box \c *this,
	 * and zero if \a p is inside the box.
	 * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&)
	 */
	template<typename Derived>
	EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
	{
		EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(p)));
	}

	/** \returns the distance between the boxes \a b and \c *this,
	 * and zero if the boxes intersect.
	 * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&)
	 */
	EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const AlignedBox& b) const
	{
		EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(b)));
	}

	/**
	 * Specialization of transform for pure translation.
	 */
	template<int Mode, int Options>
	EIGEN_DEVICE_FUNC inline void transform(
		const typename Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>::TranslationType& translation)
	{
		this->translate(translation);
	}

	/**
	 * Transforms this box by \a transform and recomputes it to
	 * still be an axis-aligned box.
	 *
	 * \note This method is provided under BSD license (see the top of this file).
	 */
	template<int Mode, int Options>
	EIGEN_DEVICE_FUNC inline void transform(const Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>& transform)
	{
		// Only Affine and Isometry transforms are currently supported.
		EIGEN_STATIC_ASSERT(Mode == Affine || Mode == AffineCompact || Mode == Isometry,
							THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS);

		// Method adapted from FCL src/shape/geometric_shapes_utility.cpp#computeBV<AABB, Box>(...)
		// https://github.com/flexible-collision-library/fcl/blob/fcl-0.4/src/shape/geometric_shapes_utility.cpp#L292
		//
		// Here's a nice explanation why it works: https://zeuxcg.org/2010/10/17/aabb-from-obb-with-component-wise-abs/

		// two times rotated extent
		const VectorType rotated_extent_2 = transform.linear().cwiseAbs() * sizes();
		// two times new center
		const VectorType rotated_center_2 =
			transform.linear() * (this->m_max + this->m_min) + Scalar(2) * transform.translation();

		this->m_max = (rotated_center_2 + rotated_extent_2) / Scalar(2);
		this->m_min = (rotated_center_2 - rotated_extent_2) / Scalar(2);
	}

	/**
	 * \returns a copy of \c *this transformed by \a transform and recomputed to
	 * still be an axis-aligned box.
	 */
	template<int Mode, int Options>
	EIGEN_DEVICE_FUNC AlignedBox
	transformed(const Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>& transform) const
	{
		AlignedBox result(m_min, m_max);
		result.transform(transform);
		return result;
	}

	/** \returns \c *this with scalar type casted to \a NewScalarType
	 *
	 * Note that if \a NewScalarType is equal to the current scalar type of \c *this
	 * then this function smartly returns a const reference to \c *this.
	 */
	template<typename NewScalarType>
	EIGEN_DEVICE_FUNC inline
		typename internal::cast_return_type<AlignedBox, AlignedBox<NewScalarType, AmbientDimAtCompileTime>>::type
		cast() const
	{
		return
			typename internal::cast_return_type<AlignedBox, AlignedBox<NewScalarType, AmbientDimAtCompileTime>>::type(
				*this);
	}

	/** Copy constructor with scalar type conversion */
	template<typename OtherScalarType>
	EIGEN_DEVICE_FUNC inline explicit AlignedBox(const AlignedBox<OtherScalarType, AmbientDimAtCompileTime>& other)
	{
		m_min = (other.min)().template cast<Scalar>();
		m_max = (other.max)().template cast<Scalar>();
	}

	/** \returns \c true if \c *this is approximately equal to \a other, within the precision
	 * determined by \a prec.
	 *
	 * \sa MatrixBase::isApprox() */
	EIGEN_DEVICE_FUNC bool isApprox(const AlignedBox& other,
									const RealScalar& prec = ScalarTraits::dummy_precision()) const
	{
		return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec);
	}

  protected:
	VectorType m_min, m_max;
};

template<typename Scalar, int AmbientDim>
template<typename Derived>
EIGEN_DEVICE_FUNC inline Scalar
AlignedBox<Scalar, AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const
{
	typename internal::nested_eval<Derived, 2 * AmbientDim>::type p(a_p.derived());
	Scalar dist2(0);
	Scalar aux;
	for (Index k = 0; k < dim(); ++k) {
		if (m_min[k] > p[k]) {
			aux = m_min[k] - p[k];
			dist2 += aux * aux;
		} else if (p[k] > m_max[k]) {
			aux = p[k] - m_max[k];
			dist2 += aux * aux;
		}
	}
	return dist2;
}

template<typename Scalar, int AmbientDim>
EIGEN_DEVICE_FUNC inline Scalar
AlignedBox<Scalar, AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const
{
	Scalar dist2(0);
	Scalar aux;
	for (Index k = 0; k < dim(); ++k) {
		if (m_min[k] > b.m_max[k]) {
			aux = m_min[k] - b.m_max[k];
			dist2 += aux * aux;
		} else if (b.m_min[k] > m_max[k]) {
			aux = b.m_min[k] - m_max[k];
			dist2 += aux * aux;
		}
	}
	return dist2;
}

/** \defgroup alignedboxtypedefs Global aligned box typedefs
 *
 * \ingroup Geometry_Module
 *
 * Eigen defines several typedef shortcuts for most common aligned box types.
 *
 * The general patterns are the following:
 *
 * \c AlignedBoxSizeType where \c Size can be \c 1, \c 2,\c 3,\c 4 for fixed size boxes or \c X for dynamic size,
 * and where \c Type can be \c i for integer, \c f for float, \c d for double.
 *
 * For example, \c AlignedBox3d is a fixed-size 3x3 aligned box type of doubles, and \c AlignedBoxXf is a dynamic-size
 * aligned box of floats.
 *
 * \sa class AlignedBox
 */

#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)                                                        \
	/** \ingroup alignedboxtypedefs */                                                                                 \
	typedef AlignedBox<Type, Size> AlignedBox##SizeSuffix##TypeSuffix;

#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix)                                                                \
	EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1)                                                                        \
	EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2)                                                                        \
	EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3)                                                                        \
	EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4)                                                                        \
	EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)

EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f)
EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d)

#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
#undef EIGEN_MAKE_TYPEDEFS

} // end namespace Eigen

#endif // EIGEN_ALIGNEDBOX_H
